%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM586+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:17:29 AM UTC 2026
% Result : Theorem 33.92s 4.77s
% Output : CNFRefutation 33.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 100 ( 23 equ)
% Maximal formula atoms : 47 ( 5 avg)
% Number of connectives : 94 ( 11 ~; 11 |; 47 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4151,axiom,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ! [W1] :
( ( ( ( ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
=> ( ( ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) )
& aSet0(W1) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| aElementOf0(W2,W1) )
& aElement0(W2) ) )
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) )
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& ! [W1] :
( ( ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(W1) ) ) )
=> aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) )
& ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
=> ( sbrdtbr0(W1) = xk
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(W1) ) ) )
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aFunction0(sdtlpdtrp0(xC,W0)) ) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
file('theBenchmark.p',m__4151) ).
fof(m__4200_02,axiom,
( aElementOf0(xx,sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))))
& ? [W0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) = xx
& aElementOf0(W0,szDzozmdt0(sdtlpdtrp0(xC,xi))) ) ),
file('theBenchmark.p',m__4200_02) ).
fof(m__,conjecture,
? [W0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) = xx
& ( ( ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W1,sdtlpdtrp0(xN,xi))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aElementOf0(W0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(W0) ) ) ) ) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) = xx
& ( ( ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W1,sdtlpdtrp0(xN,xi))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aElementOf0(W0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(W0) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_1349,negated_conjecture,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),A) != xx
| ~ aElementOf0(A,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(clausify,[status(thm)],[m___neg]) ).
fof(nnf_81,plain,
( aElementOf0(xx,sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))))
& ? [W0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) = xx
& aElementOf0(W0,szDzozmdt0(sdtlpdtrp0(xC,xi))) ) ),
inference(fof_nnf,[status(thm)],[m__4200_02]) ).
fof(sk_m__4200_02,plain,
( aElementOf0(xx,sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi))))
& sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK0) = xx
& aElementOf0(sK0,szDzozmdt0(sdtlpdtrp0(xC,xi))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_81]) ).
cnf(c_1361,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK0) = xx,
inference(split_conjunct,[status(thm)],[sk_m__4200_02]) ).
cnf(c_1362,plain,
aElementOf0(sK0,szDzozmdt0(sdtlpdtrp0(xC,xi))),
inference(split_conjunct,[status(thm)],[sk_m__4200_02]) ).
fof(m__4200,axiom,
aElementOf0(xi,szNzAzT0),
file('theBenchmark.p',m__4200) ).
cnf(c_1363,plain,
aElementOf0(xi,szNzAzT0),
inference(clausify,[status(thm)],[m__4200]) ).
cnf(c_1427,plain,
( szDzozmdt0(sdtlpdtrp0(xC,A)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A))),xk)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m__4151]) ).
cnf(c_1428,plain,
( slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A))),xk) = szDzozmdt0(sdtlpdtrp0(xC,A))
| ~ aElementOf0(A,szNzAzT0) ),
inference(copy,[status(thm)],[c_1427]) ).
cnf(c_7922,plain,
~ aElementOf0(sK0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),
inference(resolve,[status(thm)],[c_1361,c_1349]) ).
cnf(c_7925,plain,
slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk) = szDzozmdt0(sdtlpdtrp0(xC,xi)),
inference(resolve,[status(thm)],[c_1428,c_1363]) ).
cnf(c_7927,plain,
~ aElementOf0(sK0,szDzozmdt0(sdtlpdtrp0(xC,xi))),
inference(paramod,[status(thm)],[c_7925,c_7922]) ).
cnf(c_7926,plain,
$false,
inference(resolve,[status(thm)],[c_1362,c_7927]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM586+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 03:20:36 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 3761717 was started by sandbox on n012,
% 0.03/0.31 % Sat Sep 26 03:20:36 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 33.92/4.77
% 33.92/4.77 % given #500 (I,wt=36): 1340 szDzozmdt0(A) != slbdtsldtrb0(B,C) | -aElementOf0(C,szNzAzT0) | -aSubsetOf0(B,szNzAzT0) | -isCountable0(B) | -aFunction0(A) | -aSubsetOf0(sdtlcdtrc0(A,szDzozmdt0(A)),xT) | -iLess0(C,xK) | isCountable0(f28(C,B,A)). [resolve(83,a,88,e)].
% 33.92/4.77
% 33.92/4.77 % SZS status Theorem for theBenchmark
% 33.92/4.77
% 33.92/4.77 % Proof 1 at 4.13 (+ 0.12) seconds.
% 33.92/4.77 % Length of proof is 12.
% 33.92/4.77 % Level of proof is 4.
% 33.92/4.77 % Maximum clause weight is 31.000.
% 33.92/4.77 % Given clauses 540.
% 33.92/4.77
% 33.92/4.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------